We seek to bound (REF ) by applying the non-commutative Bernstein inequality for matrices [1]} to a sum of matrices given by \(\overline{\mathbf {u}_{2,\ell }}_{\Omega _2} {\mathbf {u}_{1,\ell }^\text{T}}_{\Omega _1} \mathbf {Z}\ \mathbf {F}_{1,\text{p}} \psi _{1,\ell } \psi _{2,\ell }^\text{H}\) .
Following the notation in [1]}, the operators to bound in the concentration inequality are a sequence of
\(\mathcal {Z}_\ell (\mathbf {Z}) = \overline{\mathbf {u}_{2,\ell }}_{\Omega _2} {\mathbf {u}_{1,\ell }^\text{T}}_{\Omega _1} \mathbf {Z}\ \mathbf {F}_{1,\text{p}} \psi _{1,\ell } \psi _{2,\ell }^\text{H}.\) 
